How to Calculate Voltage Drop for LV Cable Runs

Why Voltage Drop Matters

Voltage drop is the reduction in voltage that occurs along the length of a cable carrying current. In a low voltage distribution system, excessive voltage drop means the equipment at the end of the run receives less than its rated supply voltage, leading to reduced motor torque, nuisance tripping of under-voltage relays, dimming of lighting circuits, and potential overheating as motors draw higher current to compensate.

Voltage drop is a sizing criterion that operates independently of ampacity. A cable may be fully adequate to carry the load current thermally (per ampacity derating) while still producing unacceptable voltage drop, particularly on long runs, motor feeders (see motor list for FLC data), and circuits in large industrial plants where equipment can be hundreds of metres from the distribution board.

The Basic Formula

For a resistive load on a three-phase circuit, the line-to-line voltage drop is:

• VD = √3 × I × R × L

For a single-phase circuit:

• VD = 2 × I × R × L

Where:

• VD = voltage drop (volts)
• I = load current (amperes)
• R = conductor resistance per unit length (Ω per metre or Ω per 1000ft)
• L = one-way cable length (metres or feet)

The factor of √3 for three-phase accounts for the phase relationship between conductors. The factor of 2 for single-phase accounts for the return path through the neutral.

For circuits where power factor and reactance are significant (larger conductors, longer runs, or heavily inductive loads), the full phasor formula applies:

• VD = √3 × I × L × (R cosθ + X sinθ): three-phase
• VD = 2 × I × L × (R cosθ + X sinθ): single-phase

Where X is the conductor reactance per unit length and θ is the load power factor angle. For small conductors (roughly below 50 mm² or 1/0 AWG) at power factors above 0.85, the reactance term is small enough that the simplified resistive formula gives adequate accuracy. For larger conductors, include the reactance term. The resistive-only formula is a reasonable, usually conservative estimate for small conductors at high power factor, but it can understate the drop for larger conductors and at low power factor, so include reactance there.

Conductor Resistance Values

Conductor resistance varies with material, cross-section, and temperature. The two most common references are:

• NEC Chapter 9, Table 9: AC resistance in Ω per 1000 feet at 75°C conductor temperature for copper and aluminium conductors in conduit. Used for NEC-based design in North America.
• IEC 60228: conductor DC resistance at 20°C, corrected to operating temperature using a temperature coefficient (see IEC 60287-1-1). Used as the basis for IEC ampacity calculations per IEC 60364-5-52.

A selection of representative copper values. The IEC figures are DC resistance at 20°C from IEC 60228, with the equivalent at 75°C (× 1.216) in brackets; the NEC figures are Table 9 values for the nearest AWG or kcmil size, which is not an exact equivalent of the metric size:

• 4mm² copper, 4.61 Ω/km at 20°C (5.61 at 75°C) (IEC) / 1.26 Ω/1000ft (NEC equivalent ~10 AWG)
• 16mm² copper, 1.15 Ω/km at 20°C (1.40 at 75°C) (IEC) / 0.491 Ω/1000ft (NEC equivalent ~6 AWG)
• 50mm² copper, 0.387 Ω/km at 20°C (0.471 at 75°C) (IEC) / 0.154 Ω/1000ft (NEC equivalent ~1 AWG)
• 120mm² copper, 0.153 Ω/km at 20°C (0.186 at 75°C) (IEC) / 0.0608 Ω/1000ft (NEC equivalent ~4/0 AWG)
• 240mm² copper, 0.0754 Ω/km at 20°C (0.0917 at 75°C) (IEC) / 0.0258 Ω/1000ft (NEC equivalent ~500 kcmil)

Aluminium conductors have approximately 1.6× the resistance of equivalent copper cross-sections, requiring a larger conductor to achieve the same voltage drop.

Permitted Voltage Drop Limits

Neither NEC nor IEC mandates a single universal voltage drop limit, both give guidance rather than hard requirements, with the expectation that the engineer and project specification define the applicable limit.

• NEC (NFPA 70) Art. 210.19(A) and Art. 215.2(A) carry Informational Notes (called fine print notes, FPNs, in editions before 2011) recommending that voltage drop on branch circuits not exceed 3%, and that the combined voltage drop on feeder plus branch circuit not exceed 5%. Informational Notes are not mandatory. A few NEC articles do set enforceable limits for specific uses, for example fire pump circuits (Art. 695) and sensitive electronic equipment (Art. 647); check the edition adopted for your project.
• IEC 60364-5-52 (Clause 525 and Table G.52.1) gives maximum voltage drop from the origin of the installation to the load: 3% for lighting and 5% for other uses when supplied from a public LV network, and 6% and 8% when supplied from a private LV supply. Project specifications typically prescribe tighter limits, commonly 3% for lighting, 5% for power circuits, and 2.5% for sensitive equipment or instrumentation.
• Motor starting: a separate check is required for motor feeder circuits. The voltage at the motor terminals during starting must remain above a minimum level to provide adequate starting torque. Typically 80–85% of rated voltage during DOL starting is the commonly used minimum; confirm the value required by the motor manufacturer and project specification. This often governs feeder sizing for large motors on long runs.

Worked Example: Three-Phase Feeder

A 75kW motor at 480V, 0.85 power factor, 0.95 efficiency, is fed from a distribution board 120 metres away. Copper conductor in conduit. Check voltage drop for a 50mm² cable.

• Full load current: S = 75/0.95/0.85 = 92.8 kVA → I = 92,800 / (√3 × 480) = 111.7A
• Conductor resistance at 75°C: 0.387 × 1.216 = 0.471 Ω/km → r = 0.471 × 0.120 = 0.0565 Ω one-way
• VD = √3 × 111.7 × 0.0565 = 10.9V
• VD% = 10.9 / 480 × 100 = 2.28%: within the 3% limit ✓
• Maximum length at 3%: L_max = (0.03 × 480) / (√3 × 111.7 × 0.471/1000) = 158m

For the same motor at 200m, the 50mm² conductor would produce 3.79% drop, over the 3% limit. Stepping up to 70mm² (0.268 Ω/km at 20°C, 0.326 Ω/km at 75°C) gives 2.63%: compliant.

Voltage Drop on Motor Starting

During DOL starting, a motor draws its locked-rotor current (LRA), typically 6–8 times full load current (check the motor datasheet), for a few seconds. This creates a momentary voltage dip that affects not just the starting motor but all loads on the same bus.

The starting voltage drop check uses the same formula with I replaced by I_LRA. Because the starting power factor is low (typically 0.2–0.4), the full formula with reactance is more accurate; the resistive-only formula is conservative for small conductors but can understate the drop for large ones. The result must be checked against two criteria:

• Motor terminal voltage during starting ≥ 80–85% of rated voltage (to ensure adequate starting torque)
• Bus voltage dip must not cause nuisance tripping of other loads or protective relays on the same bus

If the starting voltage drop is excessive, the options are: upsize the feeder cable, change the starting method (star-delta, soft starter, or VFD), or negotiate a lower LRA motor specification with the motor vendor.

Where Standards Diverge

• Units: NEC uses feet and AWG/kcmil; IEC uses metres and mm². The calculation method is identical; only the resistance table values and length units differ. Convert carefully: 1 Ω/1000ft ≈ 3.281 Ω/km.
• Reference temperature: NEC Table 9 values are at 75°C conductor temperature; IEC 60228 gives DC resistance at 20°C which must be corrected to operating temperature (multiply by 1 + α(T − 20), where α ≈ 0.00393 for copper).
• Limit enforceability: the general NEC limits are advisory Informational Notes; some AHJs (Authorities Having Jurisdiction) treat them as mandatory. IEC limits are guidance unless the project specification makes them contractually binding. Always check the project specification before assuming which limit applies.

Summary

• Voltage drop is a sizing check independent of ampacity, both must be satisfied; the larger conductor governs
• Three-phase VD = √3 × I × R × L; single-phase VD = 2 × I × R × L
• NEC recommends ≤3% for branch circuits, ≤5% combined; IEC guidance is 3–5% (project specification governs)
• Motor feeder circuits need a separate starting voltage drop check: ensure ≥80–85% of rated voltage at motor terminals during DOL starting
• NEC uses ft / AWG / 75°C table; IEC uses m / mm² / temperature-corrected resistance: units differ, method is the same

Disclaimer: This guide is for general information and preliminary reference only. Engineering judgment is required. Verify methods, values, and code requirements against the edition adopted for your project, the project specification, and manufacturer data before use in design documents.

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